A unified framework for non-Brownian suspension flows and soft amorphous solids
While the rheology of non-Brownian suspensions in the dilute regime is well-understood, their behavior in the dense limit remains mystifying. As the packing fraction of particles increases, particle motion becomes more collective, leading to a growing length scale and scaling properties in the rheology as the material approaches the jamming transition. There is no accepted microscopic description of this phenomenon. However, in recent years it has been understood that the elasticity of simple amorphous solids is governed by a critical point, the unjamming transition where the pressure vanishes, and where elastic properties display scaling and a diverging length scale. The correspondence between these two transitions is at present unclear.
In my talk I will present a simple model of dense flow, the Affine Solvent Model (ASM). Within the ASM framework, a formal analogy can be made between the rheology and the elasticity of simple networks. This analogy leads to a new conceptual framework to relate microscopic structure to rheology. It enables us to define and compute numerically normal modes and a density of states. We find striking similarities between the density of states in flow, and that of amorphous solids near unjamming. However, a spectacular difference appears : the density of states in flow displays a single mode at a much smaller frequency scale than the one observed near unjamming. Moreover this mode governs the divergence of the viscosity.
I will show that the rheological properties depend on the elastic response of the floppy networks sampled by the dynamics. Accordingly, I will finally discuss a simple model of floppy networks which sheds light on important features of the Affine Solvent Model.